This invention relates to a high head pump-turbine having a unitary runner made up of a rigid combination of a circular plate shaped crown (upper plate), a band (lower plate), and a plurality of runner vanes which are arranged to form a circular vane cascade between the crown and band, wherein the flow path height at the outermost periphery between the crown and band is much smaller than the outermost diameter of the runner, and the runner is formed in a flattened state.
FIG. 11 of the accompanying drawings shows a general construction of a conventional high head pump-turbine. A runner 2 is secured to the lower end of a main shaft 1 which is directly connected to a generator/motor (not shown). About the runner 2 are disposed a plurality of guide vanes 3 arranged to form a stationary circular vane cascade as shown in FIG. 12. As shown in FIGS. 13 and 14, the runner 2 is formed as an integral structure including a rigid combination of a circular disc shaped crown 2a, a band 2b and a plurality of runner vanes 2c arranged as a moving circular vane cascade. The upper portion of runner 2 is covered by an upper cover 4, while the lower portion of runner 2 is covered by a lower cover 5, and a runner chamber 6 is defined between the upper and lower covers 4 and 5 for accommodating the runner 2.
When the pump-turbine is used as a turbine, high pressure water is admitted into a spiral casing 7 provided to encompass the runner 2 via stay vane 8, and guide vanes 3 to flow into the runner chamber 6. The water flows uniformly from the outside around the outer periphery of runner vanes 2c, and then flows radially inwardly through peripheral inlet paths defined between these runner vanes 2c, thereby rotating the runner 2. Thereafter, the water is discharged to the outside from the lower end of the main shaft 1 through a draft tube 9.
In a high head pump-turbine installed in a high head pumped storage power station usually having an operating head of more than 400 m, for the purpose of operating the pump-turbine at a high speed and with a small quantity of water flow as a result of high head, the runner 2 is required to have a flat characteristic construction such that the height B of the outermost flow passage between the crown 2a and band 2b is less than 0.1 times outermost peripheral diameter D.sub.O of the runner, and that the number Z.sub.R of the runner vanes 2c constituting a moving vane cascade is selected to be in a range of 6 to 8, and that the number Z.sub.G of guide vanes 3 constituting a stationary vane cascade is selected to be in a range of 12 to 32, so that Z.sub.G is larger than Z.sub.R.
During the operation of such a high head pump/turbine, as above described, the high pressure water flowing into the runner chamber 6 through guide vanes 3 constantly collides with the runner vanes 2c so that the leading edges of the runner vanes 2c in the moving vane cascade of the rotating runner 2 regularly and repeatedly pass by the trailing edge portions of the guide vanes 3 and between the vanes 3 in the stationary vane cascade. As a consequence, the runner is subjected to a regularly varying hydraulic exciting force caused by hydraulic interference between the moving vane cascade and the stationary vane cascade (see FIG. 15). Consequently, in the runner 2, due to the hydraulic exciting force mentioned above, the crown 2a and the band 2b are subjected to a disc vibration having nodes at rigid joints between the crown 2a and the band 2b and the runner vanes 26. Especially, a runner of a flat and disc type of a high head pump-turbine having a height B of the outermost peripheral flow path between the crown and band which is less than 0.1 times the outermost diameter D.sub.o, is subjected to an extremely severe vibration giving rise to a large vibration stress.
The frequency f.sub.H of the hydraulic exciting force acting on the runner 2, when it is rotated at a rated speed, is expressed by a relation Z.sub.G .multidot.N.sub.o /60 (Hz) (where N.sub.o represents the rotational speed (r.p.m.)) because the runner vanes 2c are subjected to Z.sub.G times hydraulic interference corresponding to the number of the guide vanes 3 in the stationary vane cascade during one revolution. In the case where the natural vibration frequency f.sub.N of the runner 2 is close to the frequency fx of the hydraulic excitation, the vibration stress becomes larger due to a resonance phenomenon. Even when such resonance state can be avoided under a condition in which vibration response of the runner 2 with respect to the hydraulic exciting force is large, the vibration stress nevertheless becomes large, thereby hastening runner fatigue which ultimately results in fatigue destruction of the runner 2.
For decreasing the runner vibration stress, a method of avoiding the resonance phenomenon by adjusting the natural vibration frequency f.sub.N of the runner to a level remote from the hydraulic excitation frequency f.sub.H is disclosed in Japanese Laid Open Patent Specification No. 173568/1984. However, this method is not always adequate for the actual state of the runner vibration, and can not attain its objective.
More particularly, in the prior art investigation, the manner in which the hydraulic exciting force acts on the runner and by what mechanism the vibration takes place has not been made clear. For this reason, the fundamental primary factor influencing the runner vibration and the magnitude of the vibration stress have not been correctly understood. Furthermore, it has not been made clear as to in what case the vibration stress increases and countermeasures to prevent this problem have not been developed.
We have clarified the mechanism of the runner vibration and the fundamental primary factor influencing the runner vibration and the magnitude of the vibration stress as disclosed in our technical paper presented in the JSME symposium on fluid engineering No. 900-54, entitled "Vibration Behavior of Runners of High Head Pump-Turbines (first report)", page 40-51 on Aug. 29 and 30, 1990, in Tokyo.
A summary of the technical paper is as follows:
(1) In the past, the runner vibration was considered on the assumption that the runner has the construction of a simple disc. In this paper, however we have considered that the runner consists of a disc shaped crown as a horizontal member, a disc shaped band as another horizontal member and the runner vanes as vertical members arranged to form a circular vane cascade between the two horizontal members, and that the runner is replaced by an annular Rahmen (skeleton structure) formed by a rigid combination of the horizontal and vertical members. This construction is dynamically close to the real state of the runner and thus we have studied the runner vibration.
(2) The rotating runner is subjected to a periodically varying hydraulic exciting force having an amplitude F.sub.VO on each runner vane due to the hydraulic interference (see FIG. 16) between the runner vanes 2c and the guide vanes. Denoting the center angle of the vane array spacing of the runner vane cascade by .theta..sub.R =[2.pi./Z.sub.R) and denoting an integer n[=Z-mZ.sub.R ] having a minimum absolute value of a relative difference obtained by subtracting a positive integer multiple m.multidot.Z.sub.R of Z.sub.R from Z.sub.G, the phase lag of hydraulic exciting forces acting upon adjoining two runner vanes is expressed by an equation .theta..sub.R .multidot.n[=(2.pi./Z.sub.R) (Z.sub.G -mZ.sub.R)] which is expressed by combined functions of Z.sub.G and Z.sub.R.
(3) Due to the effect of the hydraulic exciting forces acting on each of the runner vanes, a dynamic exciting bending moment which varies with the same period as the hydraulic exciting forces is applied to joints of the runner vane to the crown and band. This dynamic exciting bending moment is the product obtained by multiplying by a moment coefficient C.sub.MO the maximum producible exciting moment m.sub.o which is the runner fixed end moment arising because when the rigidity of the crown and band is extremely high, only the runner vane side assumes all of the bending deformation that should be shared by the crown, the band, and the runner vanes. Thus, the exciting bending moment of the joint parts on the joint parts on the runner vane side become M.sub.o (=C.sub.MO m.sub.o), and the exciting bending moment of the joint parts on the crown and band side becomes M.sub.o/2.
The moment coefficient C.sub.MO, that is the moment amplitude ratio (M.sub.o /m.sub.o) in which m.sub.o is taken as a reference can be given by the following theoretical equations by using a trigonometrical function cos(.sub..sub.R n) of the phase leg .theta..sub.R n of the hydraulic exciting force and a function of a rigidity ratio K.sub.R of the crown and band by taking runner vanes as a reference. EQU C.sub.MO =2K.sub.R {1+4(3K.sub.R +1).sup.2 -4(3K.sub.R +1) cos(.theta..sub.R n}.sup.1/2 /(2K.sub.R +1).multidot.(6K.sub.R +1)(1)
Denoting the thickness ratio of the crown and band to the runner vanes by t/tv and the sectional secondary moment ratio by I/I.sub.v, the rigidity ratio K.sub.R of the crown and band to the runner vanes can be calculated by the following equation. ##EQU1##
These equations show that C.sub.MO increases when the thicknesses of the crown and band are increased to increase K.sub.R and that when K.sub.R is made to be extremely large, C.sub.MO becomes 1 and M.sub.o becomes the maximum value of mo.
(4) Due to the action of the dynamic moment at the joints, the crown and band between the runner vanes accompany a disc vibration with displacement in the direction of the axis of the runner rotation wherein the joints of the crown and band to the runner vanes act as a node. Then, at each joint, vibration stress proportional to the exciting bending moment is generated.
(5) Where the damping ratio .parallel. of the vibration (c/2(mk).sup.1/2, where c represents a viscosity damping coefficient, m represents mass and k a spring constant) is made to be constant,, the magnitude of the vibration stress amplitude .DELTA..sigma. varies in direct proportion to a moment coefficient C.sub.MO (=M.sub.o /m.sub.o) representing the magnitude of the dynamic bending moment M.sub.o. The basic influencing factors on C.sub.MO are a phase lag .theta..sub.R n between the hydraulic excitations acting on adjoining two runner vanes and the rigidity ratio K.sub.R of the crown and band to the runner vanes. By decreasing K.sub.R and by keeping the phase lag .theta..sub.R n to be adequate, C.sub.MO can be decreased. Then the vibration stress .DELTA..sigma. can be decreased in direct proportion to C.sub.MO.
(6) Where the effect of the damping ratio of the vibration is taken into consideration, as the rigidity ratio K.sub.R decreases from a large value caused by the decrease of K.sub.R due to a decrease of the thicknesses of the crown and band, the damping ratio .xi. tends to increase due to the attenuation of the spring constant so that the vibration stress amplitude .DELTA..sigma. decreases to a small value less than a decreased level in direct proportional to the decrease of C.sub.MO.